1 00:00:00,040 --> 00:00:02,460 The following content is provided under a Creative 2 00:00:02,460 --> 00:00:03,870 Commons license. 3 00:00:03,870 --> 00:00:06,910 Your support will help MIT OpenCourseWare continue to 4 00:00:06,910 --> 00:00:10,560 offer high quality educational resources for free. 5 00:00:10,560 --> 00:00:13,460 To make a donation or view additional materials from 6 00:00:13,460 --> 00:00:17,390 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,390 --> 00:00:18,640 ocw.mit.edu. 8 00:00:22,120 --> 00:00:23,790 PROFESSOR: Now what I'm going to do is, I'm going to turn 9 00:00:23,790 --> 00:00:27,340 and start producer theory, OK, which will not be in the exam, 10 00:00:27,340 --> 00:00:29,830 but be the next subject to the course. 11 00:00:29,830 --> 00:00:31,850 OK, and we're going to spend a little bit longer on this. 12 00:00:31,850 --> 00:00:33,590 So what we've been doing so far is saying, look, we 13 00:00:33,590 --> 00:00:35,430 introduced the course with supply and demand curves, 14 00:00:35,430 --> 00:00:37,820 elasticities, all that. 15 00:00:37,820 --> 00:00:39,820 Hint, all that's on the exam too. 16 00:00:39,820 --> 00:00:41,220 OK, and all that. 17 00:00:41,220 --> 00:00:42,930 Then we say, well gee, where do supply and 18 00:00:42,930 --> 00:00:44,810 demand curves come from? 19 00:00:44,810 --> 00:00:47,990 Well, demand curves come from utility maximization. 20 00:00:47,990 --> 00:00:51,150 And we talked about how where indifference curves come from, 21 00:00:51,150 --> 00:00:55,380 how the tangency with the budget constraints leads to 22 00:00:55,380 --> 00:00:56,550 the demand curve. 23 00:00:56,550 --> 00:00:57,590 That's where demand curves come from. 24 00:00:57,590 --> 00:01:00,050 We talked about what underlies demand curves is income and 25 00:01:00,050 --> 00:01:01,920 substitution effects. 26 00:01:01,920 --> 00:01:05,730 OK, now let's come to supply curves. 27 00:01:05,730 --> 00:01:07,000 What underlies supply curves? 28 00:01:07,000 --> 00:01:10,390 Now on the one hand, this will be much easier than demand 29 00:01:10,390 --> 00:01:13,030 curves, because a lot of the logic is the same. 30 00:01:13,030 --> 00:01:16,100 So we can march more quickly through the analysis, because 31 00:01:16,100 --> 00:01:19,830 it's basically the same kind of tangency of curves with 32 00:01:19,830 --> 00:01:23,130 straight lines that yield supply curves that we've seen 33 00:01:23,130 --> 00:01:24,380 with consumer theory. 34 00:01:24,380 --> 00:01:28,810 On the other hand, supply curves are a ton harder, 35 00:01:28,810 --> 00:01:31,790 because now we don't just have the 36 00:01:31,790 --> 00:01:34,700 price as given to consumers. 37 00:01:34,700 --> 00:01:36,990 The suppliers actually make up the price. 38 00:01:36,990 --> 00:01:39,040 With consumers, we said the price -- you just went to the 39 00:01:39,040 --> 00:01:40,065 store. you're given a price. 40 00:01:40,065 --> 00:01:42,120 And you choose what to buy at those prices. 41 00:01:42,120 --> 00:01:43,180 Well, who set those prices? 42 00:01:43,180 --> 00:01:44,140 Producers do. 43 00:01:44,140 --> 00:01:46,560 And that's what determines the underlying supply curve. 44 00:01:46,560 --> 00:01:48,630 So life gets a little bit more difficult with producers. 45 00:01:48,630 --> 00:01:50,220 And that's why I'll probably spend about twice as many 46 00:01:50,220 --> 00:01:53,100 lectures talking about producer theory as we've spent 47 00:01:53,100 --> 00:01:56,150 talking about consumer theory. 48 00:01:56,150 --> 00:02:00,590 Now, let's go to the basics. 49 00:02:00,590 --> 00:02:06,770 The basics are, just as we had consumers making decisions, we 50 00:02:06,770 --> 00:02:08,550 thought of a consumer as somebody choosing across a 51 00:02:08,550 --> 00:02:13,000 bundle of goods, pizza versus movies, now we're going to 52 00:02:13,000 --> 00:02:17,970 think of a producer very simply as a black box, where 53 00:02:17,970 --> 00:02:21,120 inputs go in and outputs come out. 54 00:02:21,120 --> 00:02:23,250 So think of the firm. 55 00:02:23,250 --> 00:02:25,920 Let's think of a firm, a producer, as 56 00:02:25,920 --> 00:02:29,180 just some black box. 57 00:02:29,180 --> 00:02:30,820 We're literally thinking a flow chart. 58 00:02:30,820 --> 00:02:35,350 You've got inputs that go in and outputs that come out. 59 00:02:35,350 --> 00:02:39,490 And that black box, that firm, just as individuals have a 60 00:02:39,490 --> 00:02:42,470 simple goal which is to maximize their utility, 61 00:02:42,470 --> 00:02:44,690 producers have a simple goal which is to 62 00:02:44,690 --> 00:02:47,600 maximize their profits. 63 00:02:47,600 --> 00:02:52,490 And profits are defined as revenue minus cost. OK? 64 00:02:52,490 --> 00:02:57,830 Producers are these black boxes, where their goal is to 65 00:02:57,830 --> 00:03:05,760 maximize their profits, which is revenue minus cost. And the 66 00:03:05,760 --> 00:03:10,915 key to maximizing profits is efficient production. 67 00:03:16,970 --> 00:03:19,740 The key to maximizing profits is going to be to produce 68 00:03:19,740 --> 00:03:23,760 goods as efficiently as possible. 69 00:03:23,760 --> 00:03:29,000 OK, so profit maximization requires production 70 00:03:29,000 --> 00:03:30,790 efficiency. 71 00:03:30,790 --> 00:03:33,580 To maximize your profits, you need to produce as efficiently 72 00:03:33,580 --> 00:03:34,830 as possible. 73 00:03:38,040 --> 00:03:43,420 Now, you might ask yourself, gee, I can read about all 74 00:03:43,420 --> 00:03:47,570 these companies that have executive corporate jets, and 75 00:03:47,570 --> 00:03:49,750 the guys in these lavish lifestyles, and that doesn't 76 00:03:49,750 --> 00:03:52,700 seem very efficient production. 77 00:03:52,700 --> 00:03:54,140 I'll come back to that. 78 00:03:54,140 --> 00:03:56,540 OK, in a couple of lectures, we'll talk about do firms 79 00:03:56,540 --> 00:03:59,250 actually maximize profits, and whether they do or not. 80 00:03:59,250 --> 00:04:01,800 But for now, let's take as a given that they do. 81 00:04:01,800 --> 00:04:04,990 OK, just as it is a given that consumers maximize utility, 82 00:04:04,990 --> 00:04:08,270 let's take as a given that firms maximize their profits. 83 00:04:08,270 --> 00:04:09,490 OK? 84 00:04:09,490 --> 00:04:15,060 Now, to decide how to efficiently produce goods, 85 00:04:15,060 --> 00:04:17,370 we're going to turn and today discuss 86 00:04:17,370 --> 00:04:18,855 firm production functions. 87 00:04:24,160 --> 00:04:26,560 OK, today, we'll focus on production functions. 88 00:04:26,560 --> 00:04:30,960 That's essentially the technology by which a firm 89 00:04:30,960 --> 00:04:36,740 takes inputs, or what we call factors of production, and 90 00:04:36,740 --> 00:04:40,110 turns them into outputs, is through 91 00:04:40,110 --> 00:04:41,520 this production function. 92 00:04:41,520 --> 00:04:45,040 So just like your utility function is a tool for which 93 00:04:45,040 --> 00:04:49,510 we take bundles of goods and turn them into happiness, a 94 00:04:49,510 --> 00:04:51,970 production function is a tool for which we take bundles of 95 00:04:51,970 --> 00:04:54,590 inputs and turn them into outputs. 96 00:04:54,590 --> 00:04:57,030 OK, but something that's a little easier to understand 97 00:04:57,030 --> 00:04:59,330 this, you could think of a factory where stuff comes in, 98 00:04:59,330 --> 00:05:02,580 and think of a belt, a mechanical belt, going through 99 00:05:02,580 --> 00:05:04,320 and stuff goes in and other stuff comes out. 100 00:05:04,320 --> 00:05:06,840 You could think of that production function. 101 00:05:06,840 --> 00:05:09,880 We're going to think about two different kinds of inputs that 102 00:05:09,880 --> 00:05:11,000 firms are going to use. 103 00:05:11,000 --> 00:05:12,790 Once again, to make life easy, we're going to assume firms 104 00:05:12,790 --> 00:05:14,970 only use two kinds of inputs. 105 00:05:14,970 --> 00:05:18,250 Later, we'll expand this, but from mostly intuition you can 106 00:05:18,250 --> 00:05:19,560 get from thinking about this-- two kinds of 107 00:05:19,560 --> 00:05:23,760 inputs, labor and capital. 108 00:05:23,760 --> 00:05:28,590 Labor and capital are the two kinds of inputs firms use. 109 00:05:28,590 --> 00:05:30,340 Labor is clear. 110 00:05:30,340 --> 00:05:34,550 It's just hours of labor, hours of work. 111 00:05:34,550 --> 00:05:35,550 OK? 112 00:05:35,550 --> 00:05:39,140 It's just hours of work in production. 113 00:05:39,140 --> 00:05:40,820 Capital is a lot trickier. 114 00:05:40,820 --> 00:05:42,800 And we'll spend a lot of time this semester struggling with 115 00:05:42,800 --> 00:05:45,810 what capital really means. 116 00:05:45,810 --> 00:05:49,020 Basically for now, think of capital as everything else 117 00:05:49,020 --> 00:05:52,080 that goes into production, the machines, the buildings, the 118 00:05:52,080 --> 00:05:54,470 land, everything. 119 00:05:54,470 --> 00:05:56,180 Think of capital as everything else that goes into 120 00:05:56,180 --> 00:05:57,230 production. 121 00:05:57,230 --> 00:05:58,960 So basically, when you produce stuff, you produce it with 122 00:05:58,960 --> 00:06:00,740 workers working with stuff. 123 00:06:00,740 --> 00:06:01,990 Capital's the stuff. 124 00:06:04,210 --> 00:06:07,230 Now, this capital is sort of a composite of everything else 125 00:06:07,230 --> 00:06:08,590 that goes into production. 126 00:06:08,590 --> 00:06:12,540 And once again, we'll add some more detail on this later. 127 00:06:12,540 --> 00:06:18,220 OK, and the output is some output, q. 128 00:06:18,220 --> 00:06:19,600 That's the units of production. 129 00:06:19,600 --> 00:06:23,000 That's the output that is produced by the firm. 130 00:06:23,000 --> 00:06:27,910 So basically, we can think of a production function is q is 131 00:06:27,910 --> 00:06:30,810 some function of l and k. 132 00:06:30,810 --> 00:06:33,820 That's a production function, that the output you produce as 133 00:06:33,820 --> 00:06:34,670 your firm-- 134 00:06:34,670 --> 00:06:38,060 and by the way, we're going to use little q to represent a 135 00:06:38,060 --> 00:06:41,710 firm's output, and big Q to represent market output. 136 00:06:41,710 --> 00:06:45,540 OK, so little q, and if I slip in this, yell at me, OK? 137 00:06:45,540 --> 00:06:48,330 But we're going to try to consistently use little q to 138 00:06:48,330 --> 00:06:50,830 represent a given firm's output, and big Q to be the 139 00:06:50,830 --> 00:06:52,660 market's output-- 140 00:06:52,660 --> 00:06:55,700 So little q is some function of the amount of workers you 141 00:06:55,700 --> 00:06:59,080 have and the amount of capital you use. 142 00:06:59,080 --> 00:07:03,960 Now, the important distinction we're going to make here is 143 00:07:03,960 --> 00:07:10,585 between variable versus fixed inputs. 144 00:07:13,390 --> 00:07:16,850 Variable versus fixed inputs is an important distinction 145 00:07:16,850 --> 00:07:18,750 we're going to draw. 146 00:07:18,750 --> 00:07:23,210 Variable inputs are inputs that are easily changed, like 147 00:07:23,210 --> 00:07:25,580 how many hours somebody works. 148 00:07:25,580 --> 00:07:28,100 In principle, you could just have some work five hours one 149 00:07:28,100 --> 00:07:30,600 day, one hour the next day, 10 hours the day after that. 150 00:07:30,600 --> 00:07:33,290 It's easy to change hours of work. 151 00:07:33,290 --> 00:07:35,540 So that's a variable input. 152 00:07:35,540 --> 00:07:38,860 Fixed inputs are things which are harder to change quickly, 153 00:07:38,860 --> 00:07:42,010 like the size of the building that the workers 154 00:07:42,010 --> 00:07:44,540 are building in. 155 00:07:44,540 --> 00:07:46,550 Once that building's built, it's pretty hard to change it. 156 00:07:46,550 --> 00:07:49,330 You can't like lop off 2/3 of it on one day and add it back 157 00:07:49,330 --> 00:07:50,290 the next day. 158 00:07:50,290 --> 00:07:53,980 OK, that's more of the fixed inputs. 159 00:07:53,980 --> 00:07:56,080 And this will lead to a critical distinction for 160 00:07:56,080 --> 00:07:59,090 production theory, which is the short run 161 00:07:59,090 --> 00:08:00,750 versus the long run. 162 00:08:04,200 --> 00:08:05,910 The short run versus the long run. 163 00:08:05,910 --> 00:08:11,150 The long run is the period over which 164 00:08:11,150 --> 00:08:14,240 all inputs are variable. 165 00:08:14,240 --> 00:08:17,550 The short run is a period over which some inputs are fixed. 166 00:08:17,550 --> 00:08:19,380 Let me say it again, it's very important. 167 00:08:19,380 --> 00:08:21,020 The short run is the period over which 168 00:08:21,020 --> 00:08:23,180 some inputs are fixed. 169 00:08:23,180 --> 00:08:25,580 The long run is the period over which 170 00:08:25,580 --> 00:08:26,970 all inputs are variable. 171 00:08:29,530 --> 00:08:31,410 Now, what does that mean? 172 00:08:31,410 --> 00:08:33,110 I can't tell you. 173 00:08:33,110 --> 00:08:33,710 OK? 174 00:08:33,710 --> 00:08:38,590 I can tell you that, clearly, tomorrow is the short run. 175 00:08:38,590 --> 00:08:41,299 Clearly, you can't vary all your inputs over one day. 176 00:08:41,299 --> 00:08:42,940 And probably next month is the short run. 177 00:08:42,940 --> 00:08:45,670 And probably even next year is the short run. 178 00:08:45,670 --> 00:08:48,570 There's a lot of inputs that it takes more than a month to 179 00:08:48,570 --> 00:08:49,760 change, or a year to change. 180 00:08:49,760 --> 00:08:52,120 On the other hand, 10 years from now is almost certainly 181 00:08:52,120 --> 00:08:53,580 the long run. 182 00:08:53,580 --> 00:08:55,610 There's very few inputs to production you can't change 183 00:08:55,610 --> 00:08:58,120 over a 10-year period. 184 00:08:58,120 --> 00:08:59,870 So we know a day are the short run. 185 00:08:59,870 --> 00:09:01,010 And we know 10 years is the long run. 186 00:09:01,010 --> 00:09:02,610 We don't really know where the transition is, but in 187 00:09:02,610 --> 00:09:04,810 substance that doesn't matter for you guys. 188 00:09:04,810 --> 00:09:07,570 What matters is the definition of short run, long run. 189 00:09:07,570 --> 00:09:09,290 When someone asks you what the long run is, you say it's the 190 00:09:09,290 --> 00:09:11,770 period of time over which all inputs are variable. 191 00:09:11,770 --> 00:09:13,070 That's what matters. 192 00:09:13,070 --> 00:09:14,520 So it doesn't matter if you define it in days 193 00:09:14,520 --> 00:09:15,920 or months or years. 194 00:09:15,920 --> 00:09:18,465 It's a theoretical concept, which the break from the short 195 00:09:18,465 --> 00:09:21,750 run to the long run is the break between when some inputs 196 00:09:21,750 --> 00:09:24,595 are fixed and all inputs are variable. 197 00:09:24,595 --> 00:09:26,070 OK? 198 00:09:26,070 --> 00:09:28,370 Now of course, once again this is tricky. 199 00:09:28,370 --> 00:09:30,100 And economists recognize this subtlety. 200 00:09:30,100 --> 00:09:32,480 A lot of times, economists will talk about quasi-fixed 201 00:09:32,480 --> 00:09:37,020 factors of production, which are things which could change 202 00:09:37,020 --> 00:09:38,320 in between the short run and the long run. 203 00:09:38,320 --> 00:09:40,010 So for instance, take labor. 204 00:09:40,010 --> 00:09:43,760 OK, we'll talk about labor as a variable unit of production 205 00:09:43,760 --> 00:09:45,100 you can change in the short run. 206 00:09:45,100 --> 00:09:47,200 But in fact, we know in practice you can't. 207 00:09:47,200 --> 00:09:50,430 Most jobs, you can't ask the guys to come for an hour one 208 00:09:50,430 --> 00:09:52,230 day, and 10 hours the next day, five hours the day after 209 00:09:52,230 --> 00:09:55,360 that, maybe some jobs like hourly construction. 210 00:09:55,360 --> 00:09:59,040 But most jobs you guys will have, OK, your labor isn't 211 00:09:59,040 --> 00:09:59,720 that variable. 212 00:09:59,720 --> 00:10:01,340 We're typically on some kind of 213 00:10:01,340 --> 00:10:03,420 reasonably set work schedule. 214 00:10:03,420 --> 00:10:05,930 Now that work schedule can evolve. 215 00:10:05,930 --> 00:10:09,020 OK, but it can't change day by day. 216 00:10:09,020 --> 00:10:10,500 None of us are going to have jobs where they're going to 217 00:10:10,500 --> 00:10:13,000 say, look, work two hours today, 12 hours the 218 00:10:13,000 --> 00:10:14,240 next day, et cetera. 219 00:10:14,240 --> 00:10:17,260 OK, we're all going to have jobs with a fairly smooth 220 00:10:17,260 --> 00:10:17,900 distribution. 221 00:10:17,900 --> 00:10:20,990 There'll be peaks and valleys, but a fairly smooth 222 00:10:20,990 --> 00:10:22,770 distribution of our labor effort. 223 00:10:22,770 --> 00:10:26,250 So really, truly, there's very few inputs which are truly 224 00:10:26,250 --> 00:10:28,190 perfectly variable. 225 00:10:28,190 --> 00:10:29,370 OK? 226 00:10:29,370 --> 00:10:31,770 Just like there are no inputs which are truly perfectly 227 00:10:31,770 --> 00:10:35,930 fixed, but for the purposes of this model, let's think about 228 00:10:35,930 --> 00:10:38,310 labor as a variable input. 229 00:10:38,310 --> 00:10:40,370 Let's think about labor as being like hourly labor, like 230 00:10:40,370 --> 00:10:43,010 hourly construction, OK? 231 00:10:43,010 --> 00:10:45,430 And let's think about capital as being a fixed input, like a 232 00:10:45,430 --> 00:10:48,670 building that you can't pare down or rebuild overnight, but 233 00:10:48,670 --> 00:10:51,590 over a 10-year period you can. 234 00:10:51,590 --> 00:10:52,530 OK? 235 00:10:52,530 --> 00:10:55,730 Questions about that? 236 00:10:55,730 --> 00:10:57,397 Once again, we talked about simplifying assumptions at the 237 00:10:57,397 --> 00:10:58,390 beginning of the semester. 238 00:10:58,390 --> 00:11:00,700 This is our set of simplifying assumptions. 239 00:11:00,700 --> 00:11:04,320 Simplifying assumptions are that firms produce goods with 240 00:11:04,320 --> 00:11:09,070 two inputs, labor and capital, that labor is variable, which 241 00:11:09,070 --> 00:11:11,930 means you can change it minute to minute or day to day, and 242 00:11:11,930 --> 00:11:13,605 capital is fixed, which means you can only change 243 00:11:13,605 --> 00:11:16,190 it in the long run. 244 00:11:16,190 --> 00:11:19,160 OK? 245 00:11:19,160 --> 00:11:23,340 All right, so armed with that, let's now talk about how firms 246 00:11:23,340 --> 00:11:25,730 make short-run production decisions. 247 00:11:30,030 --> 00:11:32,610 And once again, these are a lot of assumptions. 248 00:11:32,610 --> 00:11:34,900 But at the end of the day, I'm going to be able to teach you 249 00:11:34,900 --> 00:11:37,830 in a couple of lectures how firms make decisions. 250 00:11:37,830 --> 00:11:39,910 And I'm going to be about 80% right. 251 00:11:39,910 --> 00:11:41,360 So that's pretty good. 252 00:11:41,360 --> 00:11:43,510 OK, so there are some assumptions, but we're going 253 00:11:43,510 --> 00:11:47,000 to go a long way with these assumptions. 254 00:11:47,000 --> 00:11:51,600 So let's start by considering the short run, and considering 255 00:11:51,600 --> 00:11:56,160 that period of time over which labor is variable 256 00:11:56,160 --> 00:11:58,970 but capital is fixed. 257 00:11:58,970 --> 00:12:01,340 Labor is variable but capital is fixed. 258 00:12:01,340 --> 00:12:04,580 That is, you have a given plant, but you can adjust how 259 00:12:04,580 --> 00:12:08,630 many workers you use every day in that plant. 260 00:12:08,630 --> 00:12:11,290 And now the firm has to decide, given that that plant 261 00:12:11,290 --> 00:12:14,210 exists, how many workers should I hire 262 00:12:14,210 --> 00:12:16,610 to produce my good? 263 00:12:16,610 --> 00:12:18,090 How many workers should I hire to produce my good? 264 00:12:18,090 --> 00:12:20,850 And the key concept that's going to determine that is 265 00:12:20,850 --> 00:12:29,350 something we'll call the marginal product of labor, 266 00:12:29,350 --> 00:12:34,580 which is the change in total output resulting from the next 267 00:12:34,580 --> 00:12:36,090 unit of labor used-- 268 00:12:36,090 --> 00:12:41,590 that is, delta q, delta l-- 269 00:12:41,590 --> 00:12:43,260 is the marginal product of labor. 270 00:12:43,260 --> 00:12:47,310 It's going to be the change in total output from another unit 271 00:12:47,310 --> 00:12:50,500 of labor, once again holding capital constant because 272 00:12:50,500 --> 00:12:51,730 that's fixed. 273 00:12:51,730 --> 00:12:56,580 So really, it's really at a given k bar, but that's 274 00:12:56,580 --> 00:12:58,780 implicit in the fact it's the short run. 275 00:12:58,780 --> 00:13:02,620 So the given level of capital, what is the change in output 276 00:13:02,620 --> 00:13:04,000 for another unit of labor? 277 00:13:04,000 --> 00:13:05,270 And once we get to the short run, I shouldn't 278 00:13:05,270 --> 00:13:05,800 have to write this. 279 00:13:05,800 --> 00:13:07,680 If I tell you short run, you should know this is true. 280 00:13:07,680 --> 00:13:12,060 But technically, we would write that out. 281 00:13:12,060 --> 00:13:17,520 Now, what we're going to do here is we're typically going 282 00:13:17,520 --> 00:13:21,280 to assume this-- 283 00:13:21,280 --> 00:13:22,600 hint, hint-- 284 00:13:22,600 --> 00:13:24,980 if you're comfortable with consumer theory, this is like 285 00:13:24,980 --> 00:13:26,680 marginal utility. 286 00:13:26,680 --> 00:13:28,660 Marginal product is like marginal utility. 287 00:13:28,660 --> 00:13:31,550 Just as the marginal utility was your utility from another 288 00:13:31,550 --> 00:13:35,650 unit of one good, holding the other good fixed, marginal 289 00:13:35,650 --> 00:13:38,860 product is the marginal production from another unit 290 00:13:38,860 --> 00:13:42,290 of an input, holding the other input fixed. 291 00:13:42,290 --> 00:13:45,520 So just sort of a parallel to keep in mind. 292 00:13:45,520 --> 00:13:49,660 And just as we've assumed and discussed the intuition for 293 00:13:49,660 --> 00:13:52,780 diminishing marginal utility, we're going to typically 294 00:13:52,780 --> 00:13:57,280 assume diminishing marginal product. 295 00:13:57,280 --> 00:14:04,340 So we're going to assume diminishing marginal product. 296 00:14:04,340 --> 00:14:10,340 That is, from a given level of labor, the next worker you add 297 00:14:10,340 --> 00:14:14,780 increases your total product by less than the previous one. 298 00:14:14,780 --> 00:14:18,290 Now once again, just like we have a non- satiation rule in 299 00:14:18,290 --> 00:14:20,180 utility, we're not going to say the next 300 00:14:20,180 --> 00:14:21,800 worker doesn't help. 301 00:14:21,800 --> 00:14:23,330 Every worker helps. 302 00:14:23,330 --> 00:14:25,920 But every worker helps less and less and less, just like 303 00:14:25,920 --> 00:14:27,880 every pizza means less and less and less to you. 304 00:14:31,510 --> 00:14:37,045 Now, the trick here, once again, this is like consumer 305 00:14:37,045 --> 00:14:38,140 theory, only more subtle. 306 00:14:38,140 --> 00:14:40,620 With consumer theory, it's pretty clear that once you had 307 00:14:40,620 --> 00:14:43,160 one pizza, clearly, the second pizza means less. 308 00:14:43,160 --> 00:14:45,680 And once you've seen one movie, your first-place prize, 309 00:14:45,680 --> 00:14:47,620 the movie you most want to see, clearly the next movie 310 00:14:47,620 --> 00:14:49,560 you want to see means a little bit less. 311 00:14:49,560 --> 00:14:51,330 Producer theory is a little more subtle. 312 00:14:51,330 --> 00:14:56,550 And you can imagine ranges over which more workers help. 313 00:14:56,550 --> 00:14:58,110 They can work together. 314 00:14:58,110 --> 00:15:00,410 So that actually two workers can do more than twice what 315 00:15:00,410 --> 00:15:03,190 one worker can do. 316 00:15:03,190 --> 00:15:04,480 And we'll talk about that. 317 00:15:04,480 --> 00:15:08,070 But we're going to focus in the main on ranges over which 318 00:15:08,070 --> 00:15:09,995 each additional worker does less and less and less. 319 00:15:12,610 --> 00:15:15,520 And the reason is because, to remember, this 320 00:15:15,520 --> 00:15:16,270 is less than two-- 321 00:15:16,270 --> 00:15:17,550 Yeah? 322 00:15:17,550 --> 00:15:21,710 AUDIENCE: Is there going to be a point where actually 323 00:15:21,710 --> 00:15:24,608 additional workers won't do anything, because of like 324 00:15:24,608 --> 00:15:27,030 constrain to the amounts of other inputs? 325 00:15:27,030 --> 00:15:29,210 PROFESSOR: Once again, we're not going to get-- just like 326 00:15:29,210 --> 00:15:32,110 there's a point at which extra pizza will make you barf-- 327 00:15:32,110 --> 00:15:34,590 OK, we're assuming we don't get to that point. 328 00:15:34,590 --> 00:15:37,610 But yes, technically of course, at some point more is 329 00:15:37,610 --> 00:15:38,090 not better. 330 00:15:38,090 --> 00:15:40,060 At some point, extra workers just sit around. 331 00:15:40,060 --> 00:15:42,110 And so I agree. 332 00:15:42,110 --> 00:15:43,840 So basically, it's a little tricky. 333 00:15:43,840 --> 00:15:45,350 You could imagine an initial range where more 334 00:15:45,350 --> 00:15:47,280 workers would help. 335 00:15:47,280 --> 00:15:49,280 Then there's the main range we'll focus on each additional 336 00:15:49,280 --> 00:15:50,845 worker does less and less and less. 337 00:15:50,845 --> 00:15:52,880 And you could imagine that running out, which is a worker 338 00:15:52,880 --> 00:15:53,660 does nothing. 339 00:15:53,660 --> 00:15:56,930 But let's just now assume we don't get there. 340 00:15:56,930 --> 00:15:59,650 So basically, what's the intuition? 341 00:15:59,650 --> 00:16:02,526 Now the intuition for in utility theory, for 342 00:16:02,526 --> 00:16:04,210 diminishing marginal utility, I thought was pretty easy, 343 00:16:04,210 --> 00:16:05,940 which is each pizza means less. 344 00:16:05,940 --> 00:16:09,010 The intuition for why each worker does less, I find a 345 00:16:09,010 --> 00:16:09,640 little bit harder. 346 00:16:09,640 --> 00:16:12,240 You could say, well, gee, why should one worker do less than 347 00:16:12,240 --> 00:16:13,120 the next worker? 348 00:16:13,120 --> 00:16:16,300 Why shouldn't the next worker do less than the first? 349 00:16:16,300 --> 00:16:19,250 And the key is this part, that we're 350 00:16:19,250 --> 00:16:21,400 holding capital constant. 351 00:16:21,400 --> 00:16:25,520 The reason each worker does less is because they only have 352 00:16:25,520 --> 00:16:28,870 the same amount of stuff to work with. 353 00:16:28,870 --> 00:16:30,870 And the classic example we use here is the example 354 00:16:30,870 --> 00:16:32,120 of digging a hole. 355 00:16:34,190 --> 00:16:36,610 You go to dig a hole and your capital's a shovel. 356 00:16:36,610 --> 00:16:38,950 And let's say for some reason the shovels are out, so you 357 00:16:38,950 --> 00:16:41,060 can't get another shovel for a while. 358 00:16:41,060 --> 00:16:42,640 OK, so there's one shovel. 359 00:16:42,640 --> 00:16:46,210 So you have one worker digging a hole, then the next worker 360 00:16:46,210 --> 00:16:47,950 comes along and that's where he can help because he can 361 00:16:47,950 --> 00:16:51,100 spell the first worker. 362 00:16:51,100 --> 00:16:53,400 And maybe the next worker's just as good because he can 363 00:16:53,400 --> 00:16:56,390 work more hours, but probably it's a little bit less good. 364 00:16:56,390 --> 00:16:58,490 But certainly by the time you add a fourth and a fifth and a 365 00:16:58,490 --> 00:17:01,390 sixth person, with one shovel, they probably each help 366 00:17:01,390 --> 00:17:03,380 because they can rotate and rest each other. 367 00:17:03,380 --> 00:17:06,550 But certainly the sixth person is not going to help dig the 368 00:17:06,550 --> 00:17:08,930 hole as much as that second person did, or the third, or 369 00:17:08,930 --> 00:17:12,430 fourth, or fifth person, because only one shovel. 370 00:17:12,430 --> 00:17:13,900 So they can share a little bit and share the 371 00:17:13,900 --> 00:17:14,980 burden a little bit. 372 00:17:14,980 --> 00:17:18,040 But at some point each additional worker helps less 373 00:17:18,040 --> 00:17:20,300 because they have to share the same shovel. 374 00:17:20,300 --> 00:17:22,780 So that's what diminishing marginal product is, because 375 00:17:22,780 --> 00:17:24,369 capital's fixed. 376 00:17:24,369 --> 00:17:26,430 With a certain amount of capital to work with, each 377 00:17:26,430 --> 00:17:28,890 additional worker just can't help as 378 00:17:28,890 --> 00:17:30,140 much as the one before. 379 00:17:32,580 --> 00:17:35,410 Now eventually, you can add more shovels. 380 00:17:35,410 --> 00:17:36,430 And you could have wheelbarrows. 381 00:17:36,430 --> 00:17:37,810 So some people could run the wheelbarrows, some people 382 00:17:37,810 --> 00:17:39,230 could run the shovels. 383 00:17:39,230 --> 00:17:40,840 But that's the long run. 384 00:17:40,840 --> 00:17:44,620 In the short run, there's the one shovel, so each additional 385 00:17:44,620 --> 00:17:47,330 worker does less good. 386 00:17:47,330 --> 00:17:49,000 And that's the intuition. 387 00:17:49,000 --> 00:17:52,460 Once again, not as clean as with consumption, where it's 388 00:17:52,460 --> 00:17:54,290 easy to see each additional pizza is worth less, because 389 00:17:54,290 --> 00:17:57,510 you could imagine the second worker might actually help. 390 00:17:57,510 --> 00:17:59,080 They could rest, et cetera, and you could imagine 391 00:17:59,080 --> 00:18:00,720 eventually the ninth worker does nothing because there's 392 00:18:00,720 --> 00:18:02,070 nothing left to do. 393 00:18:02,070 --> 00:18:04,780 But let's focus on that range where it's intuitive. 394 00:18:04,780 --> 00:18:07,500 We're staying between the second and sixth worker, which 395 00:18:07,500 --> 00:18:09,060 is when a worker would help, but they help less 396 00:18:09,060 --> 00:18:10,460 and less and less. 397 00:18:10,460 --> 00:18:13,920 OK, and that's the diminishing marginal product. 398 00:18:13,920 --> 00:18:15,170 Questions about that? 399 00:18:17,400 --> 00:18:20,176 That's short-run production. 400 00:18:20,176 --> 00:18:21,400 And we're going to come back to this. 401 00:18:21,400 --> 00:18:24,350 But I just want to introduce these concepts. 402 00:18:24,350 --> 00:18:26,900 Now let's talk about long-run production. 403 00:18:36,210 --> 00:18:39,560 Now in the long run, all inputs are variable. 404 00:18:39,560 --> 00:18:41,620 That's how we defined the long run. 405 00:18:41,620 --> 00:18:45,000 So now a firm doesn't just choose how many workers to 406 00:18:45,000 --> 00:18:47,420 hire, or how many hours of labor to buy. 407 00:18:47,420 --> 00:18:53,290 It chooses both l and k, and has to trade them off, just 408 00:18:53,290 --> 00:18:55,730 like you chose both pizzas and movies and had 409 00:18:55,730 --> 00:18:58,410 to trade them off. 410 00:18:58,410 --> 00:19:04,300 So the long-run production theory is the same, basically 411 00:19:04,300 --> 00:19:06,990 the same mechanics, as utility theory. 412 00:19:06,990 --> 00:19:08,440 There's a production function. 413 00:19:08,440 --> 00:19:09,240 You have two inputs. 414 00:19:09,240 --> 00:19:10,700 You trade them off. 415 00:19:10,700 --> 00:19:12,230 Just like you're a consumer. 416 00:19:12,230 --> 00:19:14,300 You have two goods to consume. 417 00:19:14,300 --> 00:19:15,980 You trade them off. 418 00:19:15,980 --> 00:19:19,540 The difference is going to be that ultimately production is 419 00:19:19,540 --> 00:19:20,380 going to self-- 420 00:19:20,380 --> 00:19:22,440 the difference is, when you decide how to trade them off 421 00:19:22,440 --> 00:19:25,430 as a consumer, you're given a budget constraint. 422 00:19:25,430 --> 00:19:28,620 The difference with production is the budget constraint is 423 00:19:28,620 --> 00:19:30,940 going to be itself determined by the same system. 424 00:19:30,940 --> 00:19:33,650 So you're not only going to develop your production 425 00:19:33,650 --> 00:19:35,190 function, but you're going to develop your budget constraint 426 00:19:35,190 --> 00:19:36,350 and, you're going to decide both. 427 00:19:36,350 --> 00:19:38,380 It's a little bit funky but we'll get to it. 428 00:19:38,380 --> 00:19:40,750 But for now, let's just think about the parallels to 429 00:19:40,750 --> 00:19:44,740 consumer theory, and think about a production function 430 00:19:44,740 --> 00:19:45,890 which is q-- 431 00:19:45,890 --> 00:19:46,750 little q-- 432 00:19:46,750 --> 00:19:48,880 is the square root of k times l. 433 00:19:48,880 --> 00:19:51,360 That same functional form I used with pizza and movies, 434 00:19:51,360 --> 00:19:53,590 where utility is the square root of pizza times movies. 435 00:19:53,590 --> 00:19:58,450 Now I'm going to say what you produce of your good is the 436 00:19:58,450 --> 00:20:00,310 square root of k times l. 437 00:20:00,310 --> 00:20:01,567 Now let's go to figure 8-3. 438 00:20:04,090 --> 00:20:11,520 And what we see here is, if you're trading off k and l and 439 00:20:11,520 --> 00:20:14,440 deciding to produce, then you get what's called isoquants. 440 00:20:18,210 --> 00:20:20,750 Isoquants are the parallel to indifference curves. 441 00:20:20,750 --> 00:20:22,990 Once again, this is all the same mechanics. 442 00:20:22,990 --> 00:20:27,010 Just as there were sets of goods across which you were 443 00:20:27,010 --> 00:20:31,030 indifferent, two pizzas and one movie versus one pizza and 444 00:20:31,030 --> 00:20:32,410 two movies. 445 00:20:32,410 --> 00:20:35,620 Isoquants are sets of inputs along which 446 00:20:35,620 --> 00:20:38,120 production is the same. 447 00:20:38,120 --> 00:20:41,300 So along a given isoquant, q is fixed. 448 00:20:41,300 --> 00:20:44,830 Each of those isoquants is a different level of q, but they 449 00:20:44,830 --> 00:20:49,790 show how you can vary k and l to get the same amount of q. 450 00:20:49,790 --> 00:20:52,830 So producing q equals square root of 2. 451 00:20:52,830 --> 00:20:57,120 I can use two units of capital and one unit of labor, or one 452 00:20:57,120 --> 00:20:59,990 unit of capital and two of labor. 453 00:20:59,990 --> 00:21:04,590 So I can choose lots of combinations of k and l along 454 00:21:04,590 --> 00:21:09,300 that isoquant to produce a given amount of output. 455 00:21:09,300 --> 00:21:11,390 And isoquants have all the same features as in 456 00:21:11,390 --> 00:21:12,660 indifference curves. 457 00:21:12,660 --> 00:21:15,440 The further out the better because you're producing more. 458 00:21:15,440 --> 00:21:17,040 They can't cross. 459 00:21:17,040 --> 00:21:18,830 All the same set of things we have in the indifference 460 00:21:18,830 --> 00:21:20,350 curves are true with isoquants as well. 461 00:21:24,280 --> 00:21:27,210 And they slope downwards because there's a trade off 462 00:21:27,210 --> 00:21:29,780 between capital and labor. 463 00:21:29,780 --> 00:21:33,200 Now, what's going to determine the slope of an isoquant? 464 00:21:33,200 --> 00:21:35,330 Can someone tell me what determines 465 00:21:35,330 --> 00:21:36,830 the slope of an isoquant? 466 00:21:40,670 --> 00:21:43,185 What determines if isoquants are steep or shallow? 467 00:21:47,545 --> 00:21:49,720 Well, what determines the slope of a indifference curve? 468 00:21:49,720 --> 00:21:51,540 Yes, go ahead. 469 00:21:51,540 --> 00:21:54,970 AUDIENCE: It's based on the ratio of how much labor is 470 00:21:54,970 --> 00:21:56,440 worth versus capital? 471 00:21:56,440 --> 00:21:57,500 PROFESSOR: Right, and what do we call that? 472 00:21:57,500 --> 00:21:59,170 What determines how much they're worth from each other? 473 00:21:59,170 --> 00:22:01,770 What determines the slope of a indifference curve? 474 00:22:01,770 --> 00:22:03,920 The marginal rate of substitution, it was the 475 00:22:03,920 --> 00:22:06,400 substitutability between goods. 476 00:22:06,400 --> 00:22:10,220 Likewise, the substitutability between labor and capital will 477 00:22:10,220 --> 00:22:13,550 determine the slope of these isoquants. 478 00:22:13,550 --> 00:22:19,030 So to see an example, let's do an extreme example here. 479 00:22:19,030 --> 00:22:24,370 Let's consider goods that are perfectly substitutable. 480 00:22:24,370 --> 00:22:26,420 So like, I don't know, just like a Harvard undergraduate 481 00:22:26,420 --> 00:22:27,650 and a beanie baby. 482 00:22:27,650 --> 00:22:30,980 OK, perfectly substitutable. 483 00:22:30,980 --> 00:22:34,150 Figure 8-4a shows the case of perfectly 484 00:22:34,150 --> 00:22:37,070 substitutable inputs. 485 00:22:37,070 --> 00:22:41,750 In that case, you would have a linear isoquant, because what 486 00:22:41,750 --> 00:22:44,590 that would mean is you don't care if you have three capital 487 00:22:44,590 --> 00:22:47,990 and one labor, or three labor and one capital. 488 00:22:47,990 --> 00:22:49,720 You don't care. 489 00:22:49,720 --> 00:22:53,670 You don't care if you have two labor and two capital, or 490 00:22:53,670 --> 00:22:55,310 three labor and one capital, as long as you 491 00:22:55,310 --> 00:22:56,590 get a total of four. 492 00:22:56,590 --> 00:22:58,080 That's all that matters. 493 00:22:58,080 --> 00:22:59,530 They're perfectly substitutable inputs, which 494 00:22:59,530 --> 00:23:03,890 would say that it would be something like q equals k plus 495 00:23:03,890 --> 00:23:05,550 l would be the case of perfectly 496 00:23:05,550 --> 00:23:06,640 substitutable inputs. 497 00:23:06,640 --> 00:23:09,970 You don't care if it's k or l, you just care about the total. 498 00:23:09,970 --> 00:23:11,400 That'd be perfectly substitutable inputs. 499 00:23:11,400 --> 00:23:14,590 That would be a linear isoquant. 500 00:23:14,590 --> 00:23:18,030 OK, on the other hand, let's think about goods which are 501 00:23:18,030 --> 00:23:22,020 not at all substitutable like cereal and cereal boxes. 502 00:23:22,020 --> 00:23:23,240 The cereal wouldn't be any good unless you have a 503 00:23:23,240 --> 00:23:24,330 box to put it in. 504 00:23:24,330 --> 00:23:25,480 The box doesn't do anything unless you have 505 00:23:25,480 --> 00:23:26,760 cereal to put in it. 506 00:23:26,760 --> 00:23:30,370 That would be like in 8-4b. 507 00:23:30,370 --> 00:23:34,360 8-4b would show you non-substitutable inputs where 508 00:23:34,360 --> 00:23:42,160 basically, given the amount of one input, it doesn't matter 509 00:23:42,160 --> 00:23:43,060 how much you have of the other. 510 00:23:43,060 --> 00:23:46,810 So for example, if you take these-- these we often call 511 00:23:46,810 --> 00:23:49,220 non-substitutable isoquants-- 512 00:23:49,220 --> 00:23:53,030 Leontief production functions. 513 00:23:53,030 --> 00:23:57,130 Leontief production function, for Wassily Leontief, some old 514 00:23:57,130 --> 00:23:59,000 economist. 515 00:23:59,000 --> 00:24:03,180 And basically, the Leontief production function is that 516 00:24:03,180 --> 00:24:09,520 your production, q equals the Min of k and l, is the 517 00:24:09,520 --> 00:24:11,570 Leontief production function. 518 00:24:11,570 --> 00:24:15,130 So given how much k you have, given you have 10 cereal 519 00:24:15,130 --> 00:24:19,850 boxes, once you have 10 chunks of cereal, it doesn't matter 520 00:24:19,850 --> 00:24:21,860 if you have 10, 11, 12, 1 million. 521 00:24:21,860 --> 00:24:24,590 You only have 10 cereal boxes. 522 00:24:24,590 --> 00:24:28,650 So given an amount of k, then it doesn't matter how much l 523 00:24:28,650 --> 00:24:30,970 you have. Once you get to the amount of l you need to fill 524 00:24:30,970 --> 00:24:33,960 the cereal boxes, it doesn't matter, and vice versa. 525 00:24:33,960 --> 00:24:38,270 So basically, they're perfectly non-substitutable. 526 00:24:38,270 --> 00:24:40,350 So all that determines your output is which you 527 00:24:40,350 --> 00:24:42,460 have the least of. 528 00:24:42,460 --> 00:24:45,660 OK, so substitutabilities determine the slope of the 529 00:24:45,660 --> 00:24:49,270 isoquants and of this production function. 530 00:24:49,270 --> 00:24:52,300 Now in general, we'll be in between these cases. 531 00:24:52,300 --> 00:24:54,130 There'll be some substitutability. 532 00:24:54,130 --> 00:24:56,610 Goods won't be perfectly substitutable, but they'll be 533 00:24:56,610 --> 00:24:59,060 somewhat substitutable. 534 00:24:59,060 --> 00:25:01,370 So in general, we'll be in between these cases. 535 00:25:01,370 --> 00:25:04,690 And more generally, just as the slope of the indifference 536 00:25:04,690 --> 00:25:08,020 curve is the marginal rate of substitution, the slope of the 537 00:25:08,020 --> 00:25:10,620 isoquant we will call the marginal rate of technical 538 00:25:10,620 --> 00:25:13,060 substitution. 539 00:25:13,060 --> 00:25:14,690 The marginal rate of technical substitution-- the rate at 540 00:25:14,690 --> 00:25:17,910 which you can substitute one input for another in a 541 00:25:17,910 --> 00:25:21,500 production function is the marginal rate of technical 542 00:25:21,500 --> 00:25:22,750 substitution-- 543 00:25:24,510 --> 00:25:35,900 which we'll define as delta k, delta l for a given q bar, the 544 00:25:35,900 --> 00:25:38,870 rate at which you can trade off k for l 545 00:25:38,870 --> 00:25:40,955 to hold q bar fixed. 546 00:25:44,990 --> 00:25:48,035 Now, as with marginal rate of substitution, the marginal 547 00:25:48,035 --> 00:25:49,990 rate of technical substitution will 548 00:25:49,990 --> 00:25:51,780 change along the isoquant. 549 00:25:51,780 --> 00:25:56,690 So if you go to figure 8-5, here we've drawn a typical 550 00:25:56,690 --> 00:26:00,680 isoquant for the production function q equals square root 551 00:26:00,680 --> 00:26:03,100 of k times l. 552 00:26:03,100 --> 00:26:04,490 So the production function is q equals the square 553 00:26:04,490 --> 00:26:05,590 root of k times l. 554 00:26:05,590 --> 00:26:06,910 And here's a isoquant. 555 00:26:06,910 --> 00:26:09,580 This is the isoquant of all combinations 556 00:26:09,580 --> 00:26:11,335 which produce two units. 557 00:26:11,335 --> 00:26:15,320 This is the q equals 2 isoquant. 558 00:26:15,320 --> 00:26:17,770 Now, unlike utility-- remember utility?-- 559 00:26:17,770 --> 00:26:20,620 we said where u equals 2 was meaningless. 560 00:26:20,620 --> 00:26:22,980 Utility was an ordinal concept, 561 00:26:22,980 --> 00:26:24,150 not a cardinal concept. 562 00:26:24,150 --> 00:26:26,780 Here, quantity is meaningful. 563 00:26:26,780 --> 00:26:28,730 If you produce four, you would have only produced twice as 564 00:26:28,730 --> 00:26:30,130 much as if you produced two. 565 00:26:30,130 --> 00:26:32,300 We can care about both the ordinality and the cardinality 566 00:26:32,300 --> 00:26:33,790 of these outcomes. 567 00:26:33,790 --> 00:26:37,690 So we can say, what are the combinations of inputs which 568 00:26:37,690 --> 00:26:38,970 lead you to produce two units? 569 00:26:38,970 --> 00:26:40,890 What's all these combinations of inputs? 570 00:26:40,890 --> 00:26:43,040 So whereas you can have one unit of labor and four units 571 00:26:43,040 --> 00:26:46,695 of capital, two of each, or four units of labor and one 572 00:26:46,695 --> 00:26:48,420 unit of capital, all will produce two 573 00:26:48,420 --> 00:26:49,640 units of the output. 574 00:26:49,640 --> 00:26:52,560 And what you can see is that the marginal rate of technical 575 00:26:52,560 --> 00:26:53,750 substitution varies. 576 00:26:53,750 --> 00:26:57,770 So for instance, when we start with four units of capital and 577 00:26:57,770 --> 00:27:01,580 one unit of labor, and we think about adding a second 578 00:27:01,580 --> 00:27:05,040 unit of labor, then the marginal rate of technical 579 00:27:05,040 --> 00:27:07,230 substitution is minus 2. 580 00:27:07,230 --> 00:27:11,290 That is, one unit of labor is worth two units of capital. 581 00:27:11,290 --> 00:27:14,020 In other words, we can produce the same amount of widgets of 582 00:27:14,020 --> 00:27:19,740 q, but if we replace two units of capital with one unit of 583 00:27:19,740 --> 00:27:23,490 labor, so at that point we're very capital-intensive, and 584 00:27:23,490 --> 00:27:26,790 that unit of labor is very valuable. 585 00:27:26,790 --> 00:27:31,290 On the other hand, now if you imagine we're down at 4-1, at 586 00:27:31,290 --> 00:27:32,650 the third point-- 587 00:27:32,650 --> 00:27:35,050 we are probably using a, b, c-- 588 00:27:35,050 --> 00:27:37,980 now we're at the third point, where you have we have four 589 00:27:37,980 --> 00:27:40,680 units of labor and one unit of capital. 590 00:27:40,680 --> 00:27:46,640 Now, if you'd be willing to give up two units of labor 591 00:27:46,640 --> 00:27:48,836 just to get one unit of capital, that's the marginal 592 00:27:48,836 --> 00:27:52,110 rate of technical substitution is now minus 1/2. 593 00:27:52,110 --> 00:27:54,330 When you're very labor-intensive, you'd be 594 00:27:54,330 --> 00:27:57,550 happy to give up a lot of labor to get a little capital. 595 00:27:57,550 --> 00:28:00,490 Once again, the principle of diminishing marginal product, 596 00:28:00,490 --> 00:28:02,830 just like the principle of diminishing marginal utility, 597 00:28:02,830 --> 00:28:07,050 implies that the marginal rate of technical substitution is 598 00:28:07,050 --> 00:28:10,770 going to be falling as you go down the isoquant. 599 00:28:10,770 --> 00:28:12,920 Just like the marginal rate of substitution fell as you went 600 00:28:12,920 --> 00:28:15,460 down the indifference curve, the marginal rate of technical 601 00:28:15,460 --> 00:28:19,895 substitution is going to fall as you go down the isoquant. 602 00:28:23,530 --> 00:28:24,590 And why is this? 603 00:28:24,590 --> 00:28:27,180 Once again it's because of this diminishing marginal 604 00:28:27,180 --> 00:28:28,220 productivity. 605 00:28:28,220 --> 00:28:32,440 That is, as you add more and more labor, given capital, 606 00:28:32,440 --> 00:28:34,770 each unit of labor can do less and less. 607 00:28:34,770 --> 00:28:36,800 And likewise, as you add more and more capital, given an 608 00:28:36,800 --> 00:28:38,550 amount of workers to use it, each unit of capital can do 609 00:28:38,550 --> 00:28:39,820 less and less. 610 00:28:39,820 --> 00:28:43,750 So it's a very different approach, but gets you the 611 00:28:43,750 --> 00:28:47,890 same answer, which is with consumption, each piece does 612 00:28:47,890 --> 00:28:51,010 less and less for you, but we can see that as consumers. 613 00:28:51,010 --> 00:28:54,000 Here's the notions of labor, each worker does less and less 614 00:28:54,000 --> 00:28:55,610 for you, holding capital fixed. 615 00:28:55,610 --> 00:28:58,300 And each machine by the same logic, if you have one guy in 616 00:28:58,300 --> 00:28:59,620 the hole, it doesn't matter how many 617 00:28:59,620 --> 00:29:01,010 shovels you throw there. 618 00:29:01,010 --> 00:29:02,770 He still is only one guy. 619 00:29:02,770 --> 00:29:05,860 So each machines is doing less and less by the same logic. 620 00:29:05,860 --> 00:29:08,980 And those diminishing marginal products lead to this 621 00:29:08,980 --> 00:29:10,880 decreasing marginal rate of technical substitution as you 622 00:29:10,880 --> 00:29:12,130 move along the isoquant. 623 00:29:14,390 --> 00:29:16,002 That's about the most technical statement I'll make 624 00:29:16,002 --> 00:29:17,600 all semester. 625 00:29:17,600 --> 00:29:21,480 OK, questions about that, about what's going on here? 626 00:29:21,480 --> 00:29:23,490 That's production theory. 627 00:29:23,490 --> 00:29:26,660 That's what you need to know to know basically how firms 628 00:29:26,660 --> 00:29:28,210 produce things. 629 00:29:28,210 --> 00:29:31,000 Now, what we're going to do is, now take this basic 630 00:29:31,000 --> 00:29:35,910 production theory, and turn it into actually understanding 631 00:29:35,910 --> 00:29:38,990 how firms make decisions on how much to produce. 632 00:29:38,990 --> 00:29:40,990 But before we do that, I want to talk about one other 633 00:29:40,990 --> 00:29:45,340 concept, which is very important for thinking about 634 00:29:45,340 --> 00:29:46,790 production theory. 635 00:29:46,790 --> 00:29:48,990 And it comes back to these assumptions that we make which 636 00:29:48,990 --> 00:29:51,480 might be a little bit unrealistic, which is the 637 00:29:51,480 --> 00:29:54,330 concept of returns to scale. 638 00:30:00,050 --> 00:30:01,575 The concept of returns to scale. 639 00:30:05,410 --> 00:30:10,220 So here the question is, what happens if we increase all 640 00:30:10,220 --> 00:30:12,300 inputs proportionally? 641 00:30:12,300 --> 00:30:13,740 Return to scale. 642 00:30:13,740 --> 00:30:16,870 By scale, I mean, what if we just double everything, twice 643 00:30:16,870 --> 00:30:19,400 as much labor and twice as much capital. 644 00:30:19,400 --> 00:30:21,660 That's an increase in scale, increasing all inputs 645 00:30:21,660 --> 00:30:25,530 proportionally, twice as much labor, twice as much capital, 646 00:30:25,530 --> 00:30:27,660 half as much labor, half as much capital. 647 00:30:27,660 --> 00:30:32,160 So a change in scale is an equal increase or decrease in 648 00:30:32,160 --> 00:30:34,060 all inputs? 649 00:30:34,060 --> 00:30:35,300 Equal proportional. 650 00:30:35,300 --> 00:30:41,390 So what happens if we increase all inputs, increase or 651 00:30:41,390 --> 00:30:45,600 decrease proportionally? 652 00:30:45,600 --> 00:30:47,960 And this is an interesting case, because it's like, OK, 653 00:30:47,960 --> 00:30:49,890 what if we just make the firm half as big? 654 00:30:49,890 --> 00:30:51,140 What happens? 655 00:30:53,140 --> 00:30:55,530 Well, the answer is, it depends on 656 00:30:55,530 --> 00:30:57,490 the production process. 657 00:30:57,490 --> 00:31:02,660 Some production processes will exhibit what we call constant 658 00:31:02,660 --> 00:31:04,970 returns to scale. 659 00:31:04,970 --> 00:31:06,390 This is a convenient form. 660 00:31:06,390 --> 00:31:08,550 It's convenient because the way constant returns to scale 661 00:31:08,550 --> 00:31:16,930 works is, it says that f of 2l, 2k, is equal to 2 662 00:31:16,930 --> 00:31:21,050 times f of l, k. 663 00:31:21,050 --> 00:31:24,060 That is, if it's constant, you can just pull the 2 out. 664 00:31:24,060 --> 00:31:27,920 Doubling the inputs leads to doubling the outputs, which 665 00:31:27,920 --> 00:31:30,510 equals to 2q, I'll write here. 666 00:31:30,510 --> 00:31:33,510 Doubling the inputs equals doubling the outputs. 667 00:31:33,510 --> 00:31:36,700 So if I have twice as much labor and capital, that's the 668 00:31:36,700 --> 00:31:38,980 same as twice producing what I had with the original labor 669 00:31:38,980 --> 00:31:41,970 and capital which will get me twice the original production. 670 00:31:41,970 --> 00:31:43,940 That's the constant returns to scale. 671 00:31:43,940 --> 00:31:47,400 So every time I double my firm, I get exactly twice as 672 00:31:47,400 --> 00:31:50,140 much stuff out. 673 00:31:50,140 --> 00:31:54,030 We can contrast that with increasing returns to scale, 674 00:31:54,030 --> 00:32:01,530 IRS, which says that f of 2l, 2k, is greater than 2 675 00:32:01,530 --> 00:32:05,380 times f of l, k. 676 00:32:05,380 --> 00:32:08,620 Or it's greater than 2q. 677 00:32:08,620 --> 00:32:11,400 That is, when I double my firm, I produce more than 678 00:32:11,400 --> 00:32:13,580 twice as much stuff. 679 00:32:13,580 --> 00:32:15,240 That'd be increasing returns to scale. 680 00:32:17,790 --> 00:32:20,000 On the other hand, we could also have decreasing returns 681 00:32:20,000 --> 00:32:23,420 to scale, which not surprisingly means that f of 682 00:32:23,420 --> 00:32:31,970 2l, 2k, is less than 2 times f of l, k, or less than 2q. 683 00:32:34,590 --> 00:32:37,620 That would be decreasing returns to scale, which is 684 00:32:37,620 --> 00:32:42,010 when I double my firm I get less than twice as much stuff. 685 00:32:42,010 --> 00:32:47,345 Can anyone give me an example or some reason why returns to 686 00:32:47,345 --> 00:32:50,340 scale is going to be increasing or decreasing? 687 00:32:50,340 --> 00:32:51,910 Think about firms out there. 688 00:32:51,910 --> 00:32:54,090 Give me some that, by returns to scale, would be increasing 689 00:32:54,090 --> 00:32:56,360 or decreasing, any examples you can think of. 690 00:32:56,360 --> 00:32:57,260 There's no right answer here. 691 00:32:57,260 --> 00:32:58,320 Yeah. 692 00:32:58,320 --> 00:32:58,780 Go ahead, on the end. 693 00:32:58,780 --> 00:33:02,372 AUDIENCE: Oh, if you're mining something, you can only get to 694 00:33:02,372 --> 00:33:05,007 stuff at one time, so having more equipment and more people 695 00:33:05,007 --> 00:33:07,390 doesn't mean you can get more out of it? 696 00:33:07,390 --> 00:33:09,590 PROFESSOR: Right, so if there's a limited resource, 697 00:33:09,590 --> 00:33:11,150 you could imagine decreasing returns to scale. 698 00:33:11,150 --> 00:33:11,320 Good. 699 00:33:11,320 --> 00:33:12,250 What else? 700 00:33:12,250 --> 00:33:12,982 Yeah. 701 00:33:12,982 --> 00:33:15,184 AUDIENCE: If the company gets harder to manage, that could 702 00:33:15,184 --> 00:33:17,710 be decreasing returns to scale? 703 00:33:17,710 --> 00:33:19,440 PROFESSOR: Right, exactly. 704 00:33:19,440 --> 00:33:23,760 If you're an entrepreneur, you've got a great idea, but 705 00:33:23,760 --> 00:33:25,460 it turns out that idea only works if you really are 706 00:33:25,460 --> 00:33:26,520 hands-on about it. 707 00:33:26,520 --> 00:33:28,640 You're not Mark Zuckerberg, who can just farm the thing 708 00:33:28,640 --> 00:33:29,830 out, it's really your idea. 709 00:33:29,830 --> 00:33:30,730 And you've got to be there. 710 00:33:30,730 --> 00:33:32,500 Then after it expands and you lose control of the 711 00:33:32,500 --> 00:33:34,900 production, it might not be as effective because you're not 712 00:33:34,900 --> 00:33:36,850 there making it happen. 713 00:33:36,850 --> 00:33:37,900 Any ideas why return-- 714 00:33:37,900 --> 00:33:38,730 Yeah. 715 00:33:38,730 --> 00:33:40,170 AUDIENCE: If you or [UNINTELLIGIBLE] 716 00:33:45,460 --> 00:33:46,050 PROFESSOR: So that's an example of 717 00:33:46,050 --> 00:33:47,490 increasing returns to scale. 718 00:33:47,490 --> 00:33:50,820 Increasing returns to scale would be, gee, maybe if I'm 719 00:33:50,820 --> 00:33:55,760 bigger, I can get a better deal on the inputs. 720 00:33:55,760 --> 00:33:58,570 But that's not quite right, because we haven't really got 721 00:33:58,570 --> 00:33:59,650 into prices yet. 722 00:33:59,650 --> 00:34:01,280 I'm looking-- that's really a market response-- 723 00:34:01,280 --> 00:34:03,370 I'm looking for a more technological story, a 724 00:34:03,370 --> 00:34:04,810 technological story of increasing returns. 725 00:34:04,810 --> 00:34:05,390 Go ahead. 726 00:34:05,390 --> 00:34:07,115 AUDIENCE: If you're bigger, you can hire a specialist to 727 00:34:07,115 --> 00:34:11,310 do work, like a manager who can [INAUDIBLE] 728 00:34:11,310 --> 00:34:11,810 PROFESSOR: Exactly. 729 00:34:11,810 --> 00:34:14,290 So it's the opposite, which is, let's say you have an idea 730 00:34:14,290 --> 00:34:16,840 which is pretty good, but in fact it's replicable. 731 00:34:16,840 --> 00:34:21,560 And right now, you're trying to manage some guys. 732 00:34:21,560 --> 00:34:23,239 And then all of a sudden, when you get twice as big, you 733 00:34:23,239 --> 00:34:26,050 bring other people in who can effectively replicate your 734 00:34:26,050 --> 00:34:28,929 idea, and really expand it in a very effective way. 735 00:34:28,929 --> 00:34:32,370 You can have increasing returns to scale. 736 00:34:32,370 --> 00:34:34,850 Now, so an example of what that looks like, if you go to 737 00:34:34,850 --> 00:34:42,070 the last page in the handout, figure 8-6a shows constant 738 00:34:42,070 --> 00:34:43,340 returns to scale. 739 00:34:43,340 --> 00:34:45,020 So let's start with 8-6a, that's 740 00:34:45,020 --> 00:34:46,429 constant returns to scale. 741 00:34:46,429 --> 00:34:49,190 So here-- and these are from the textbook-- 742 00:34:49,190 --> 00:34:52,830 for example, when we doubled the inputs from 100 labor, 100 743 00:34:52,830 --> 00:34:57,480 capital, to 200 labor, 200 capital, you doubled output. 744 00:34:57,480 --> 00:34:59,480 Those are constant returns to scale isoquants. 745 00:34:59,480 --> 00:35:01,300 The last page shows decreasing and 746 00:35:01,300 --> 00:35:03,010 increasing returns to scale. 747 00:35:03,010 --> 00:35:05,670 So for instance, tobacco is an example of decreasing returns 748 00:35:05,670 --> 00:35:09,710 to scale, because there's only so much leaf that you have 749 00:35:09,710 --> 00:35:11,820 that you can produce. 750 00:35:11,820 --> 00:35:15,260 So here, when you double the inputs from 100 to 200, your 751 00:35:15,260 --> 00:35:18,930 output only goes from 100 to 142. 752 00:35:18,930 --> 00:35:20,950 OK, and if you want to double the 200 units, you've got to 753 00:35:20,950 --> 00:35:23,320 go way the heck up there on inputs. 754 00:35:23,320 --> 00:35:26,310 On the other hand, primary metal production is something 755 00:35:26,310 --> 00:35:28,550 where you can have increasing returns to scale, because 756 00:35:28,550 --> 00:35:32,460 there's such high costs of building a plant that once 757 00:35:32,460 --> 00:35:36,860 it's built, so just like I said, gee, in fact that second 758 00:35:36,860 --> 00:35:38,170 digger of the hole might actually make it more 759 00:35:38,170 --> 00:35:38,770 productive. 760 00:35:38,770 --> 00:35:41,700 Once that plant's built, there's one worker banging 761 00:35:41,700 --> 00:35:43,790 around the plant, a second worker adds a huge amount to 762 00:35:43,790 --> 00:35:45,740 productivity because they can specialize. 763 00:35:45,740 --> 00:35:47,400 Basically, increasing returns to scale is going to come from 764 00:35:47,400 --> 00:35:48,900 specialization. 765 00:35:48,900 --> 00:35:51,380 So if you build this big plant to build primary, to build 766 00:35:51,380 --> 00:35:54,630 steel, one worker in that plant is no good, because he's 767 00:35:54,630 --> 00:35:55,960 got to pour the steel, then run over and 768 00:35:55,960 --> 00:35:57,080 cool it down, et cetera. 769 00:35:57,080 --> 00:35:59,168 Once you have two, they can specialize, and three, they 770 00:35:59,168 --> 00:36:00,470 can specialize more. 771 00:36:00,470 --> 00:36:01,840 You might think of something like that would have 772 00:36:01,840 --> 00:36:04,310 increasing returns to scale through specialization. 773 00:36:04,310 --> 00:36:08,040 And that's illustrated here, where doubling the inputs 774 00:36:08,040 --> 00:36:10,410 actually leads to more than doubling the output. 775 00:36:10,410 --> 00:36:12,300 Now we're going to talk about all these cases. 776 00:36:12,300 --> 00:36:15,140 Typically, economists are suspicious of increasing 777 00:36:15,140 --> 00:36:16,350 returns to scale. 778 00:36:16,350 --> 00:36:20,400 Anybody, anybody who ever has an IPO, whoever starts a firm 779 00:36:20,400 --> 00:36:21,230 will always tell you that they have 780 00:36:21,230 --> 00:36:22,530 increasing returns to scale. 781 00:36:22,530 --> 00:36:24,750 Well, we say, I've got a great idea and the bigger, the more, 782 00:36:24,750 --> 00:36:26,420 the better it's going to be. 783 00:36:26,420 --> 00:36:28,680 And they're generally wrong. 784 00:36:28,680 --> 00:36:30,920 Generally, we think of increasing returns to scale as 785 00:36:30,920 --> 00:36:32,510 being like a free lunch. 786 00:36:32,510 --> 00:36:33,855 And we don't like free lunches, we economists. 787 00:36:33,855 --> 00:36:36,640 We think, gee, if it's really increasing returns to scale, 788 00:36:36,640 --> 00:36:38,400 you would have already expanded there. 789 00:36:38,400 --> 00:36:40,332 OK, if it's really such a good idea to get bigger, why aren't 790 00:36:40,332 --> 00:36:42,470 you bigger already? 791 00:36:42,470 --> 00:36:43,470 Now, it doesn't mean you can-- 792 00:36:43,470 --> 00:36:43,720 Yeah. 793 00:36:43,720 --> 00:36:44,930 AUDIENCE: Well, they need capital. 794 00:36:44,930 --> 00:36:46,480 PROFESSOR: Well, they need capital, and so that would be 795 00:36:46,480 --> 00:36:46,980 their argument. 796 00:36:46,980 --> 00:36:47,620 And that's great. 797 00:36:47,620 --> 00:36:48,910 And typically, they're wrong. 798 00:36:48,910 --> 00:36:51,010 But that would be why you would argue that they need 799 00:36:51,010 --> 00:36:51,990 capital to get bigger. 800 00:36:51,990 --> 00:36:54,170 So typically, we like decreasing returns to scale. 801 00:36:54,170 --> 00:36:55,590 That's going to be our sort of default 802 00:36:55,590 --> 00:36:56,520 assumption of the world. 803 00:36:56,520 --> 00:37:00,560 In other words, here's a way to think about it, think about 804 00:37:00,560 --> 00:37:03,255 we're dealing with mature firms. We're modeling, for 805 00:37:03,255 --> 00:37:04,070 instance, mature firms. 806 00:37:04,070 --> 00:37:06,680 We think that for mature firms, at least, there's not 807 00:37:06,680 --> 00:37:08,470 increasing returns to scale, because in a mature firm they 808 00:37:08,470 --> 00:37:09,410 would have hit that point already. 809 00:37:09,410 --> 00:37:11,640 Now they're on the decreasing part. 810 00:37:11,640 --> 00:37:13,360 So that's where we're going to focus for 811 00:37:13,360 --> 00:37:14,370 the rest of the semester. 812 00:37:14,370 --> 00:37:16,090 OK, let me stop there. 813 00:37:16,090 --> 00:37:18,120 And good luck tomorrow night. 814 00:37:18,120 --> 00:37:19,350 And we'll come back to talk more about 815 00:37:19,350 --> 00:37:20,600 production on Wednesday.